Tail pieces have been widely used in the plumbing industry for insertion in a waste pipe which conducts waste water to a waste drain. One form of tail piece includes a portion for conducting the waste water from appliances into the waste pipe for delivery to the waste drain system. Another form of tail piece includes a portion which diverts a part of the waste water to a floor drain water trap for priming the latter. Up to the present time, it has been necessary to provide tail pieces which are of different construction, the particular tail piece to be used being determined by the use thereof either as a drain for waste water from appliances or as a primer for a floor drain water trap.